How can I prevent registry editing without my applications permission?

I think you're going to face a lot of trouble trying to do this, but you're welcome to try. There are a few things that you should think of, though:

The security in Vista and before that was not much to write home about, but in 7 it's a little different. Here, applications have to ask permission (using the System.IO.Permissions namespace if I'm not mistaken) amongst other thing to write in the registry or certain parts of it, and if the application doesn't have the correct permissions, a dialog will be shown asking if it's ok.

That means that if you succeed in making your application, the user will get TWO alerts at the same time (because I don't think it's possible to disable the internal permissions system).

Also, you might want to ask yourself if your application should protect the WHOLE registry or only certain parts...

Good luck